非定常对流扩散问题的非协调局部投影有限元方法  

NONCONFORMING LOCAL PROJECTION STABILIZED METHOD FOR THE NON-STATIONARY CONVECTION DIFFUSION PROBLEM

作　　者：常晓蓉[1] 冯民富[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《计算数学》2011年第3期275-288,共14页Mathematica Numerica Sinica

基　　金：四川省科技攻关课题(编号:05GG006-006-2)资助项目

摘　　要：本文将近年来基于协调有限元逼近提出的涡旋粘性法推广应用到非协调有限元逼近,对非定常的对流占优扩散问题,空间采用非协调Crouzeix-Raviart元逼近,时间用Crank-Nicolson差分离散格式,提出了Crank-Nicolson差分-局部投影法稳定化有限元格式,我们对稳定性和误差估计给出了详细的分析,得出了最优的估计.This paper is concerned with the extension of the conforming element approximations based on eddy viscosity to the nonconforming element approximation. For the non-stationary convection diffusion problem, where the Crouzeix-Raviart element is employed. A fully discretized formulation with a Crank-Nicholson scheme for the time variable, and a Crank- Nicholson difference - local projection method finite element scheme is prensented.We prove stability and convergence, then an optimal error estimate is obtained.

关 键 词：局部投影 非协调有限元 非定常对流占优扩散问题 

分 类 号：O241.82[理学—计算数学]